On the classical capacity of quantum Gaussian measurement

Abstract

In this paper we consider the classical capacity problem for Gaussian measurement channels without imposing any kind of threshold condition. We prove Gaussianity of the average state of the optimal ensemble in general and discuss the Hypothesis of Gaussian Maximizers concerning the structure of the ensemble. The proof uses an approach of Wolf, Giedke and Cirac adapted to the convex closure of the output differential entropy. Then we discuss the case of one mode in detail, including the dual problem of accessible information of a Gaussian ensemble. In quantum communications there are several studies of the classical capacity in the transmission scheme where not only the Gaussian channel but also the receiver is fixed, and the optimization is performed over certain set of the input ensembles. These studies are practically important in view of the complexity of the optimal receiver in the Quantum Channel Coding (HSW) theorem. Our findings are relevant to such a situation where the receiver is Gaussian and concatenation of the channel and the receiver can be considered as one Gaussian measurement channel. Our efforts in this and preceding papers are then aimed at establishing full Gaussianity of the optimal ensemble (usually taken as an assumption) in such schemes.